Yes, you would but remember that you would only need to file a tax return for Kentucky because those states have reciprocal agreements with each other. What that means is that these agreements provide for taxpayers to be taxed by their state of residence, and not the state where income is earned.
For more information on reciprocal states, you can visit the TurboTax article below:
https://ttlc.intuit.com/replies/3299954